9. Conclusion

We have presented a selection of essential elements of the theory of nonlinear dynamical systems (in particular chaos theory), including recently developed elements (reconstruction of equations of motion, topological characterization). This theory works on systems with a small number of degrees of freedom.

Furthermore, the heat equation is often coupled with equations from fluid mechanics. The result is a system of nonlinear partial differential equations that inherently generates an infinite number of degrees of freedom, in contradiction with the requirements of system dynamics. In many cases, however, an infinite number of modes are damped so that the observed behavior can effectively be described using a small number of degrees of freedom.

These ideas...